The men, one of whom never turned up at his regiment and two of whom deserted, are the first to be jailed for evading military conscription since Sweden reinstated national service.
André, 20, who was given a 14-day sentence for leaving his regiment shortly after training began, said he felt it was wrong that he be punished.
“I think that it's up to me to decide. If I don't want to do it, I shouldn't be forced,” he told Sveriges Radio.
But Bengt Forssten, head of division at the Swedish Defence Recruitment Agency, said those conscripted could not simply change their minds.
“Having regrets or your motivation changing isn't an acceptable reason to drop out of your service,” he said.
Sweden's parliament voted to bring back conscription in 2017 as part of a national effort to rebuild the country's defence capability in response to a more militaristic Russia. About 3,700 young people were signed up to serve last year, and this year as many as 5,000 are expected to be called up.
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According to the Swedish news agency TT, at least 24 young people have been convicted of draft-dodging since conscription was brought back, with the overwhelming majority receiving fines.
A further 260 people have broken off their training for other reasons, such as being wounded or a desire not to bear arms.
André said he had left his regiment when they took a break during training.
“It was during a break for water that I never came back. I just sat there in the room,” he told Sveriges Radio. “All I could think was that I didn't want to be there.”
He received his sentence on March 1st.